Finite Group Databasebeta

← C107×#8733 #41034697

Subgroups — C107×#8733 #41034697

Order 27392.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2298C211yesmaximal, characteristic
2C107×#1458C212yesmaximal
3C107×#1276C212yesmaximal, complemented
4C107×#1274C212yesmaximal, complemented
5C2×#117×C107C2211yescharacteristic
6#431×C107C2214yes—
7#388×C107—22no—
8#387×C107—22no—
9C4×C4⋊C4×C107C412yes—
10C4×C22⋊C4×C107C412yes—
11#376×C107C2211yescharacteristic
12C43×C107C2211yescharacteristic
13#324×C107—22no—
14#323×C107—22no—
15C23×C4×C107C2×C411yescharacteristic
16#117×C107—22no—
17#117×C107—22no—
18C2×C4⋊C4×C107—22no—
19C2×C4⋊C4×C107D412yes—
20C2×C22⋊C4×C107—22no—
21C2×C22⋊C4×C107D412yes—
22C2×C42×C107—22no—
23C2×C42×C107C2×C412yes—
24C2×C42×C107C2×C412yes—
25C2×C42×C107C2×C411yescharacteristic
26C2×C42×C107C2311yescharacteristic
27C4⋊C8×C107—24no—
28C22⋊C8×C107—24no—
29C4×C8×C107—24no—
30#95×C107—22no—
31#95×C107—22no—
32#95×C107—22no—
33C24×C107C22⋊C411yescharacteristic
34C22×C4×C107—22no—
35C22×C4×C107—21no—
36C22×C4×C107—21no—
37C22×C4×C107—24no—
38C22×C4×C107—22no—
39C22×C4×C107C22⋊C411yescharacteristic
40C22×C4×C107C22⋊C412yes—
41C22×C4×C107C22×C411yescharacteristic
42C22×C4×C107C2×D412yes—
43C2×C8×C107—44no—
44C4⋊C4×C107—24no—
45C4⋊C4×C107—44no—
46C22⋊C4×C107—24no—
47C22⋊C4×C107—44no—
48C42×C107—21no—
49C42×C107—21no—
50C42×C107—24no—
51C42×C107—24no—
52C42×C107—44no—
53C42×C107#4112yes—
54C42×C107#4112yes—
55C23×C107—21no—
56C23×C107—22no—
57C23×C107—42no—
58C23×C107C2×C22⋊C411yescharacteristic
59C2×C4×C107—24no—
60C2×C4×C107—22no—
61C2×C4×C107—21no—
62C2×C4×C107—22no—
63C2×C4×C107—42no—
64C2×C4×C107—42no—
65C2×C4×C107—42no—
66C2×C4×C107—42no—
67C2×C4×C107—42no—
68C2×C4×C107—42no—
69C2×C4×C107—42no—
70C2×C4×C107—42no—
71C2×C4×C107—42no—
72C2×C4×C107#11711yescharacteristic
73C2×C4×C107#11711yescharacteristic
74C2×C4×C107#12314yes—
75C2×C4×C107#13114yes—
76C8×C107—84no—
77C22×C107—22no—
78C22×C107—41no—
79C22×C107—42no—
80C22×C107—82no—
81C22×C107#38111yescharacteristic
82C22×C107#40812yes—
83C4×C107—24no—
84C4×C107—44no—
85C4×C107—41no—
86C4×C107—42no—
87C4×C107—82no—
88C4×C107#43312yes—
89C4×C107#43312yes—
90#8733C10711yesmaximal, characteristic, direct product factor, Sylow
91C2×C107—22no—
92C2×C107—81no—
93C2×C107#181811yescharacteristic
94C2×C107#182712yes—
95#2298C2×C10711yescharacteristic
96#1458C2×C10712yes—
97#1276C2×C10712yescomplemented
98#1274C2×C10712yescomplemented
99C107#873311yescharacteristic, direct product factor, Sylow
100C2×#117C22×C10711yescharacteristic
101#431C22×C10714yes—
102#388—22no—
103#387—22no—
104C4×C4⋊C4C4×C10712yes—
105C4×C22⋊C4C4×C10712yes—
106#376C22×C10711yescharacteristic
107C43C22×C10711yescharacteristic
108#324—22no—
109#323—22no—
110C23×C4C2×C4×C10711yescharacteristic
111#117—22no—
112#117—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4D4×C10712yes—
115C2×C22⋊C4—22no—
116C2×C22⋊C4D4×C10712yes—
117C2×C42—22no—
118C2×C42C2×C4×C10712yes—
119C2×C42C2×C4×C10712yes—
120C2×C42C2×C4×C10711yescharacteristic
121C2×C42C23×C10711yescharacteristic
122C4⋊C8—24no—
123C22⋊C8—24no—
124C4×C8—24no—
125#95—22no—
126#95—22no—
127#95—22no—
128C24C22⋊C4×C10711yescharacteristic
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4C22⋊C4×C10711yescharacteristic
135C22×C4C22⋊C4×C10712yes—
136C22×C4C22×C4×C10711yescharacteristic
137C22×C4C2×D4×C10712yes—
138C2×C8—44no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C22⋊C4—24no—
142C22⋊C4—44no—
143C42—21no—
144C42—21no—
145C42—24no—
146C42—24no—
147C42—44no—
148C42#41×C10712yes—
149C42#41×C10712yes—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊C4×C10711yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4#117×C10711yescharacteristic
168C2×C4#117×C10711yescharacteristic
169C2×C4#123×C10714yes—
170C2×C4#131×C10714yes—
171C8—84no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22#381×C10711yescharacteristic
177C22#408×C10712yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4#433×C10712yes—
184C4#433×C10712yes—
185C2—22no—
186C2—81no—
187C2C107×#181811yescharacteristic
188C2C107×#182712yes—
subgroupG/H
centerC2×C4×C107#117
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#381
prime radicalC24×C107C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ #376×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C107×#1276C2semidirect
4. C107×#1274C2semidirect
90. #8733C107direct (N × H)
97. #1276C2×C107semidirect
98. #1274C2×C107semidirect
99. C107#8733direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C107×#22982
C107×#14582
C107×#12762
C107×#12742
#8733107